Statement-1: If A is an orthogonal matrix of order n, then $adj (adj\, A) |=±1$
Statement-2: $|adj (adj\, A)| = |A|^{n^2 – 1}$
Answer & explanation
Correct answer: option 3
We have known that $|adj (adj\, A)| = |A|^{(n − 1)^2}$.
So, statement-2 is false.
If A is an orthogonal matrix, then $|A|= ±1$
$∴|adj (adj\, A)|=|A|^{(n-1)^2} =(±1)^{(n-1)^2}=±1$